eXEQ, the EXED (E,q)-range calculator for the elastic mode:

Version 0.16 has been released in March 2017. The instrument has been equipped with a vacuum chamber, new detectors and a new chopper, resulting in changes to the rotation angle limits and detector shadowing. The rotation angle is now restricted to a range from -12° to +2.5°.

It is now possible to specify h, k, l values as a range, for example 1:3 instead of h. This will override the internal range-finding algorithm and fix the range in the output plot to the range specified in the input field.

The magnet rotation angle can now be specified as a floating point number, although the detector positions are still fixed to integral values. Therefore, the results for non-integral magnet rotation angles are still approximate.

This software has been developed at Helmholtz-Zentrum Berlin, in order to assist the users of the Extreme-Environment Diffractometer (EXED) combined with the High-Field Magnet (HFM).

The HFM may apply over 25 T constant magnetic field to the sample mounted inside. However, at the same time it limits the available space around the sample. Therefore, it becomes necessary to plan the sample alignment carefully, so that the desired Bragg reflections may be observed in the experiment.

We encourage EXED users to specify the lattice parameters of their sample, and try out different sample orientations (by means of vectors . Bu and Bv), to see if the reflections of interest are within the instrument's range. The magnet itself may be rotated by at most 15° in each direction, which additionally extends the covered range. However, please note that as the neutron guide enters the magnet cone and the cryostat, the real rotation limits are lower, and in the most commonly used setup on EXED, with the focussing guide and cryostat on the backscattering side, the real limits are -12° to 2.5°. Also, the choice of the neutron wavelength band is essential for the measurement.

FEATURE 1: Following a popular request we implemented 3 rotation angles that make it possible to reorient the sample quickly. This, however, does not reflect the real capabilities of the instrument at the moment.

FEATURE 2: The intensity is now expressed as an absolute value, derived from the instrument spectrum and chopper frequency settings. Therefore, for the intensity to be correct, the wavelength resolution must be specified by the user.

FEATURE 3: Instead of marking the shadows of the sample enviroment on the resolution map, it is now possible to see the detector panels directly in a separate plot. It is also possible to plot the peaks in real space on the detector panels. The peak will not be marked if it is outside of the angular range of the detector. If it is within the angular range, but outside of the wavelength band, it will be marked with 0 intensity.

The parameters

Wavelength.

In any experiment on EXED, the beam is polychromatic and the neutron wavelengths are distributed around a mean value. This is selected by the Bandwidth Chopper (BC). The width of the band may be at most 14.6 Å (BC at 5 Hz), and at least 0.6 Å (BC at 120 Hz). The mean value of the wavelength is determined by the settings of chopper phases. The usable range of the instrument is typically from λ = 0.7 Å to λ ≈ 15.0 Å, although longer wavelengths may be used as well, at the expense of longer measurement times.

Sample.

The sample definition is limited to the lattice constants and angles. The orientation is defined in respect to the magnetic field direction. Therefore, if the magnet axis is aligned along the incoming beam (magnet rotation is 0°), then the vectors Bu and Bv are the same as the conventional orientation vectors u and v. The information about the sample is then used to re-calculate the real-space coordinates of the detector pixels into the reciprocal space positions expressed by Miller indices h, k, l.

Magnet orientation.

The magnet may be rotated to extend the coverage of the scattering angles, but ultimately the rotation range is limited by the size of the magnet cone and the sample environment. As the magnet is rotated, the forward detector banks are moved simultaneously, while the backward detectors may only be switched between 2 static positions. For this reason some pixels of the backward detectors will be shadowed by the magnet cone.

Input fields

Wavelength-range minimum [Å], wavelength-range maximum [Å]:

The beginning (λmin and end (λmax) of the wavelength band. Then the wavelength is defined as λmin < λ < λmax .

OR

Wavelength-range centre [Å], wavelength-range bandwidth [Å]:

The mean value (λmean) of the wavelength and the width (w) of the wavelength band. Then the wavelength is defined as λmean - w/2 < λ < λmean + w/2.

Wavelength resolution:

The requested value of wavelength resolution, Δλ/λ. It determines the absolute neutron flux output by the software. It also determines the Pulse Chopper type (double-disc or Fermi) and the Pulse Chopper and Bandwidth Chopper rotation speeds (in Hz). The resolution applies to the mean wavelength of the specified band; therefore, the calculated chopper frequencies will change significantly with the wavlength band.

Lattice constants [Å], lattice angles [°]:

The definition of the lattice parameters. As the space group is not considered here, effectively each sample should be considered P1.

Orientation vector Bu, orientation vector Bv: Similar to conventional u and v, Bu is the sample Bragg reflection coinciding with the magnet axis, and Bv is the sample Bragg reflection in-plane, perpendicular to the magnet axis. The actual u and v are calculated by the code and indicated in the output. In particular, the plot of the detector position illustrates the direction of u, v, Bu and Bv.

Magnetic field direction [°]:

The magnet is rotated around the sample position by this angle. The range depends on the settings of the guide and sample environment.

Sample rotation angles [°]:

FOR TESTING PURPOSES ONLY, we have added the possibility to rotate the sample around the vectors Bu, Bv and Bw, the last being the cross product of the former two. The current sample environment does not allow any of the three rotations, although at least one of them may become possible in the future.

H, K, L:

These parameters determine what part of the reciprocal space will be mapped. For H=h, K=k, L=l, the entire range in the reciprocal space will be shown. For H=h K=0.23 L=l a cut of the reciprocal space will be created, showing the (h 0.23 l) plane. For H=3:5 K=0.23 L=l a cut of the reciprocal space will be created, showing the (h 0.23 l) plane, with h restricted to values between 3 and 5. At the moment only the planes perpendicular to the main axes are allowed.

Marked points (H K L):

If it is of interest, a specific set of reflections may be marked in the plots of the reciprocal space. If, for example, the reflection (3.5 0 2.23) is input as a marked point, its position will then be marked on the plot, and its position in respect to the area covered by the instrument can be seen. If the point is within range, a label indicating the relative intensity of the neutron beam at that point will be output as well.

Precision:

The precision parameter scales the resolution of the output images. The number of pixels along the axis is defined as 100 times the current value of precision. If setting the precision alone does not produce an image that is accurate enough, it is still possible to narrow down the output range of h, k or l by specifying the limits in the input fields. As an example, to see the surroundings of the (1 1 1) peak exactly, one could set precision to 3, and request H=0.5:1.5 K=0.5:1.5 L=1 .

Output

Instrument orientation.

An image of the detector positions in respect to the sample. It is included to allow a better understanding of the instrument's operation. The shadows of the magnet cone, beam stop, guide housing and the sample enviroment are added to the plot as grey shapes, while the accessible part of each detector tube is marked in red. The color of the inaccessible zones in this plot matches the color of the corresponding areas in the reciprocal space coverage plots. The effect of the rotation angles on the direction of the Bu and Bv vectors is illustrated here also.

Reciprocal space coverage.

The main output of the program. After the sample has been defined, it is possible to adjust the parameters of the instrument (wavelength, magnet rotation, sample orientation) until the desired Bragg reflections appear in the range covered by the detectors. As it is, the process is to a certain extent based on trial and error. The intensity of the color in the plot of the accessible range corresponds to the intensity of the neutron beam at the sample, and is based on real measurement results from EXED. The wavelength resolution setting chosen by the user affects the intensity, as it, together with the wavlength band, determines the current chopper frequencies.

Detector panels.

This is a visualisation of the detector panels in real space, in cylindrical coordinates. Using this option it is possible to see the shadows of the sample environment and beam stop on the panels, as well as identify the position of a specific Bragg peak on the detector. If the peak is within range on the map of the reciprocal-space coverage, it will also be marked on the detector panel view triggered by this button.

There are currently 4 detector panels in the forward direction, numbered 1, 3, 5 and 6 in the software, while the panels in the backward direction are still labelled 2 and 4, same as before. To make it easier to see which panels contribute to the instrument coverage in a given setting, it is possible to deactivate the panels by removing their numbers from the 'Active' input field.

Chopper frequencies.

Once the sample has been aligned correctly and the wavelength band chosen, one can find out what resolution will be available in the experiment for those parameters, and what chopper settings are necessary to obtain it.

Conclusion

We hope that you find this software useful. For greater control over the output (and improved speed), you might also consider trying the stand-alone version, available for download from the HFM/EXED website.

Good luck planning your experiment!


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